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Transformer coupled toroidal wave-heated remote plasma sources operating in Ar/NF 3 mixtures

Remote plasmas are used in semiconductor device manufacturing as sources of radicals for chamber cleaning and isotropic etching. In these applications, large fluxes of neutral radicals (e.g. F, O, Cl, H) are desired with there being negligible fluxes of potentially damaging ions and photons. One remote plasma source (RPS) design employs toroidal, transformer coupling using ferrite cores to dissociate high flows of moderately high pressure (up to several Torr) electronegative gases. In this paper, results are discussed from a computational investigation of moderate pressure, toroidal transformer coupled RPS sustained in Ar and Ar/NF 3 mixtures. Operation of the RPS in 1 Torr (133 Pa) of argon with a power of 1.0 kW at 0.5 MHz and a single core produces a continuous toroidal plasma loop with current continuity being maintained dominantly by conduction current. Operation with dual cores introduces azimuthal asymmetries with local maxima in plasma density. Current continuity is maintained by a mix of conduction and displacement current. Operation in NF 3 for the same conditions produces essentially complete NF 3 dissociation. Electron depletion as a result of dissociative attachment of NF 3 and NF x fragments significantly alters the discharge topology, confining the electron density to the downstream portion of the source where the NFx density has been lowered by this dissociation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Efficient analysis of magnetic field line behavior in toroidal plasmas

The confinement of plasmas in tokamaks and stellarators depends on magnetic field lines lying in nested toroidal surfaces. The transition near the plasma edge away from the lines lying in magnetic surfaces defines properties of divertors. The transition in time defines properties of disruptions. Divertor design and disruption analyses require a detailed understanding of these transitions. The use of a Fourier transform coupled with a Gaussian window function allows far more information to be extracted about these transitions using far shorter field line integrations than can be obtained using traditional methods based on Poincaré plots. The physics of divertors and disruptions is reviewed to clarify why the type of information that can be gained from more efficient methods of analysis is of central importance to the fusion program based on magnetic confinement.

Boozer, Allen H. [Columbia Univ., New York, NY (Un↗

Modeling of the ECCD injection effect on the Heliotron J and LHD plasma stability

The aim of the study is to analyze the stability of the energetic particle modes (EPM) and Alfven Eigenmodes (AE) in Helitron J and LHD plasma if the electron cyclotron current drive (ECCD) is applied. Additionally, the analysis is performed using the code FAR3d that solves the reduced MHD equations describing the linear evolution of the poloidal flux and the toroidal component of the vorticity in a full 3D system, coupled with equations of density and parallel velocity moments for the energetic particle (EP) species, including the effect of the acoustic modes. The Landau damping and resonant destabilization effects are added via the closure relation. The simulation results show that the n = 1 EPM and n = 2 global AE (GAE) in Heliotron J plasma can be stabilized if the magnetic shear is enhanced at the plasma periphery by an increase (co-ECCD injection) or decrease (ctr-ECCD injection) of the rotational transform at the magnetic axis ($\rlap{-} \iota_{0}$). In the ctr-ECCD simulations, the EPM/AE growth rate decreases only below a given $\rlap{-} \iota_{0}$, similar to the ECCD intensity threshold observed in the experiments. In addition, ctr-ECCD simulations show an enhancement of the continuum damping. The simulations of the LHD discharges with ctr-ECCD injection indicate the stabilization of the n = 1 EPM, n = 2 toroidal AE (TAE) and n = 3 TAE, caused by an enhancement of the continuum damping in the inner plasma leading to a higher EP β threshold with respect to the co- and no-ECCD simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

W7-X and the sawtooth instability: towards realistic simulations of current-driven magnetic reconnection

Magnetic reconnection in W7-X is studied by means of global numerical simulations in a series of models of increasing complexity. The magnetic geometry ranges from that of a cylinder to the full three-dimensional field of W7-X, and the equations solved range from ideal magnetohydrodynamics (MHD) to gyrokinetics. We simulate plasmas from the first operation phase with electron cyclotron current drive (ECCD). These are characterized by an equilibrium magnetic field featuring an ECCD-distorted 'humped' profile of the rotational transform ι, with ι = 1 in two radial locations. Such plasmas generally show sawtooth activity, hence motivating the present study. We pay particular attention to the role of equilibrium current density gradients in the destabilization of reconnecting modes. When the equilibrium temperature and density gradients are artificially suppressed (to eliminate the pressure gradient drive), the perturbed electrostatic potential is radially localized between the locations at which ι = 1. This is shown with a purely collisionless gyrokinetic model, in cylindrical geometry. In the real toroidal geometry of W7-X, for a non-ideal MHD model including a uniform resistivity, electron inertia and (numerical) viscosity, the same qualitative behaviour is observed. In particular, even if a resonant (m, n) = (1, -1) perturbation is initialized, the most unstable mode is the (m, n) = (-4, 4), where m and n are the poloidal and toroidal mode numbers, respectively. Other modes are destabilized due to geometric coupling. The growth rate of this instability scales as η 1/3 , where η is the plasma resistivity, thus suggesting that ECCD drives ideal MHD stable W7-X plasmas towards non-ideal marginality. An ideal magnetohydrodynamic analysis confirms the result. A fluid-kinetic hybrid version of the EUTERPE code shows that gyrokinetic ions have a stabilizing effect on these modes. For W7-X relevant collisionalities, the growth rate scales linearly with the electron skin depth, d e . Implications of our results for sawtoothing W7-X operation are discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Directional finite difference method for directly solving 3D gyrokinetic field equations with enhanced accuracy

The gyrokinetic (GK) field equation is a three-dimensional (3D) elliptic equation, but it is often simplified to a set of two-dimensional (2D) equations by assuming that the field does not vary along a specific direction. However, this simplification can introduce inevitable 0th-order numerical errors, as nonlinear mode coupling in toroidal geometry can produce undesirable harmonic modes that violate the assumption. In this work, we propose a novel directional finite difference method (FDM) with a local coordinate transformation to better resolve the target field of interest. The directional FDM can accurately solve 3D GK field equations without simplifications, which can overcome the limitations of conventional methods. The accuracy and efficiency of different FDMs are analyzed in great detail for a variety of geometries, from simple 2D Cartesian coordinates to realistic 3D curvilinear coordinates. The 0th-order numerical errors of simplified 2D GK equations were found to be more problematic for low-harmonic modes and low aspect ratio geometries such as spherical tokamaks. On the other hand, the directional 3D FDM can accurately resolve a much wider range of harmonic modes aligned to the direction of interest, including the low-harmonic modes. In conclusion, we demonstrate that the directional 3D FDM is a highly effective algorithm for solving the 3D GK field equations, achieving accuracy improvements of 10 to 100 times or more, particularly for low-harmonic modes in spherical tokamaks.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Initial Development of Fusion Magnet Simulation Capabilities for Performance and Safety Evaluation Using the MOOSE Framework

Fusion energy holds the promise of being a transformative technology as a carbon-neutral, sustainable source of energy. Whole device modeling and the development of fusion digital twins will be increasingly important for emerging fusion device concepts at both national laboratories and within the commercial fusion industry. However, meeting the challenge of whole device modeling of fusion energy devices requires robust, multiphysics, multiscale modeling and simulation technologies capable of running on large-scale supercomputers. Detailed analysis of individual systems at-scale is also required to ensure safe and efficient operation as well as provide the safety basis for future device designs and licensing activities. In a tokamak, toroidal and poloidal magnets confine and shape the fusion plasma to promote the fusion reaction. High plasma temperatures and high magnetic field requirements in modern design concepts (leading to high amounts of energy stored within each magnet) impose electrical, thermal, and mechanical loads on the magnet components, which in turn impacts the safety considerations of the magnet and their supporting systems. Idaho National Laboratory (INL) has a history of working in this space, including development and benchmarking of the Magnetic System Circuitry Analysis Program (MSCAP) and Magnet Arcing (MAGARC) codes to study magnet quench events; notably, MAGARC was used to study quenching during the ITER Engineering Design Activity. However, these legacy codes and capabilities are not parallel and scalable, and new tools are required for future advances in this area, which leads to the INL-developed Multiphysics Object-Oriented Simulation Environment (MOOSE) framework. Developed originally for fission reactor systems under United States Department of Energy, Office of Nuclear Energy modeling and simulation programs, the MOOSE framework has been well-suited to multiscale, multiphysics modeling and simulation needs for nuclear systems. The framework is open-source, well-tested, under continuous development and deployment, and developed to a Nuclear Quality Assurance, Level 1 software quality standard. MOOSE has also been used in the fusion space previously in several projects: INL’s Tritium Migration Analysis Program, Version 8 (TMAP8) for tritium migration, UK Atomic Energy Authority’s A Unified Resource for OpenMC (fusion) Reactor Applications (AURORA) code for fusion thermo-mechanical and neutronics analysis, and Argonne National Laboratory’s Cardinal for high-fidelity computational fluid dynamics and neutronics. However, to model superconducting magnets, several MOOSE enhancements are required: additions to the current MOOSE electromagnetic capabilities, new material libraries for superconductors of interest (such as YBCO), as well as fusion-specific models for thermo-mechanics. This talk will discuss initial development activities to build these capabilities in MOOSE, focusing on initial validation and benchmarking activities. Proposed coupling workflows and future work to support the simulation of fusion magnets and magnet structural assemblies for performance and safety evaluation in MOOSE will also be discussed.

70 - PLASMA PHYSICS AND FUSION TECHNOLOGY↗